A119806 Decimal expansion of cos(gamma).
8, 3, 7, 9, 8, 5, 2, 8, 7, 8, 8, 0, 1, 9, 6, 5, 3, 9, 9, 5, 4, 9, 9, 2, 8, 6, 1, 2, 5, 8, 9, 4, 9, 7, 2, 4, 8, 0, 8, 6, 5, 9, 2, 0, 1, 3, 2, 4, 1, 7, 6, 6, 5, 7, 9, 0, 4, 1, 1, 7, 8, 9, 3, 5, 5, 6, 7, 7, 6, 9, 3, 6, 8, 8, 8, 0, 2, 6, 2, 2, 2, 3, 2, 7, 5, 4, 9, 4, 1, 4, 6, 8, 6, 5, 4, 2, 1, 9, 1, 7, 5, 6, 8, 2, 3
Offset: 0
Examples
0.8379852878801965399549928612589497248086592013241766579...
Links
- G. C. Greubel, Table of n, a(n) for n = 0..10000
- D. M. Bătineţu-Giurgiu and Neculai Stanciu, Problem UP.328, Romanian Mathematical Magazine, Vol. 30, Autumn edition (2021), p. 114; Solutions, by Mokhtar Khassani-Mostaganem and Marian Ursărescu.
- D. M. Bătineţu-Giurgiu, Neculai Stanciu, and José Luis Díaz-Barrero, The Last Three Decades of Lalescu Limit, Arhimede Mathematical Journal, Vol. 7, No. 1 (2020), pp. 16-26. See Problem 7, pp. 23-24.
- Toyesh Prakash Sharma, The Applications of the Stirling's approximation to find limits, Revista Electronica MateInfo.ro, December 2020, pp. 44-49. See Problem 4, p. 46.
Programs
-
Magma
SetDefaultRealField(RealField(100)); R:= RealField(); Cos(EulerGamma(R)); // G. C. Greubel, Aug 30 2018
-
Mathematica
RealDigits[Cos[EulerGamma],10,150][[1]]
-
PARI
default(realprecision, 100); cos(Euler) \\ G. C. Greubel, Aug 30 2018
Formula
Equals 2 * e * lim_{n->oo} (sin(gamma(n))-sin(gamma))*(n!)^(1/n), where gamma(n) = Sum_{k=1..n} 1/k - log(n) (Bătineţu-Giurgiu, 2021). - Amiram Eldar, Apr 02 2022
Comments